The effect of bluntness on the drag of spherical-tipped truncated cones of fineness ratio 3 at Mach numbers 1.2 to 7.4

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Title:
The effect of bluntness on the drag of spherical-tipped truncated cones of fineness ratio 3 at Mach numbers 1.2 to 7.4
Series Title:
NACA RM
Physical Description:
18 p. : ill. ; 28 cm.
Language:
English
Creator:
Sommer, Simon C
Stark, James A
Ames Research Center
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

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Subjects / Keywords:
Drag (Aerodynamics)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
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federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: The drag of spherically blunted conical models of fineness ratio 3 was investigated in the Ames super-sonic free-flight wind tunnel at Mach numbers from 1.2 to 7.4 in the Reynolds number range from 1.0 x 10⁶ to 7.5 x 10⁶. The models tested had bluntness ratios of nose diameter to base diameter from 0 to 0.50. The use of small amounts of bluntness for minimizing drag and the drag penalties associated with large bluntnesses are discussed.
Bibliography:
Includes bibliographic references (p. 7).
Statement of Responsibility:
by Simon C. Sommer and James A. Stark.
General Note:
"Report date April 25, 1952."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003810613
oclc - 133685056
sobekcm - AA00006199_00001
System ID:
AA00006199:00001

Full Text
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SKESEARCH MEMORANDUM

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TRUNCATED CONES OF FINENESS RATIO 3 AT

MACH NUMBERS 1.2 TO 7.4

By Simon C. Sommer and James A. Stark

Ames Aeronautical Laboratory
Moffett Field, Calif.


UNIVERSITY OP FLORIDA
DOCUMENTS N*RTMENT
120 MARSON SCIENCE LIUSARY
P.O. BQX 117011
GANEVILLE, FL 32611-7011 USA


TIONAL ADVISORY COMMITTEE

FOR AERONAUTICS
WASHINGTON
April 25, 1952


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NACA RM A52B13


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH MEMORANDUM


THE EFFECT OF BLUNTNESS ON THE DRAG OF SPHERICAL-TIPPED

TRUNCATED CONES OF FINENESS RATIO 3 AT

MACH NUMBERS 1.2 TO 7.4

By Simon C. Sommer and James A. Stark


SUMMARY


The drag nf spherically blunted conical models of fineness ratio 3
was investigated at Mach numbers from 1.2 to 7.4 in the Reynolds number
range from 1.0 x 106 to 7.5 x 106. Results of the tests showed that
slightly blunted models had less drag than cones of the same fineness
ratio throughout the Mach number range. At Mach numbers less than 1.5,
drag penalties due to large bluntnesses were moderate but these became
severe with increasing Mach number.

Wave drag obtained by the method of Munk and Crown, in which the
wave drag is determined by integrating the momentum loss through the head
shock wave, showed that the wave drag and total drag followed the same
trends with increasing bluntness. Wave drag was also estimated by com-
bining the experimental wave drag of a hemisphere with the theoretical
wave drag of a conical afterbody, and this estimate of wave drag is
believed to be adequate for many engineering purposes.


INTRODUCTION


Blunt noses are being considered for some supersonic vehicles for
the purpose of housing guidance equipment. In some cases a high degree
of bluntness is required, and the drag penalty due to this bluntness may
be significant. On the other hand, work done by others indicated that
slightly blunt noses will have less drag than pointed noses of the same
fineness ratio. For these two reasons the drag of blunt-nose shapes is
of current interest and therefore an investigation was made in the Ames
supersonic free-flight wind tunnel to determine the influence of blunt-
ness on drag at Mach numbers from 1.2 to 7.4. The models tested were
truncated cones with spherical noses having bluntness ratios of nose







NACA RM A52B13


diameter to base diameter from 0 to 0.50. All models had a fineness
ratio of length to base diameter of 3.


SYMBOLS


A frontal area of model, square feet

CD total drag coefficient total drag)

1CD total drag penalty compared to the cone (CDmodel CDone)

CDb base drag coefficient base drag
C, q.A /

CDf skin-friction drag coefficient (skin-friction drag)
1 \qA
CDv total drag coefficient based on volume to the two-thirds power

total drag
qV2/3

CD, wave drag coefficient (wave drag

d diameter of the base, feet

dn diameter of the nose, feet

M free-stream Mach number

q free-stream dynamic pressure, pounds per square foot

R free-stream Reynolds number, based on axial length of model

V volume of model, cubic feet


MODELS


The models tested were truncated circular cones with tangentially
connected spherical nose segments, as shown in figure l(a). All models
had a fineness ratio of 3, with base diameters and lengths of 0.45 and
1.35 inches, respectively. The models had holes bored in their bases for
aerodynamic stability. Five different shapes were tested with nose diam-
eters of 0, 7-1/2 percent, 15 percent, 30 percent, and 50 percent of the
base diameter.







NACA RM A52B13


The models were constructed of 75-ST aluminum alloy. The maximum
measured dimensional deviations were as follows: nose diameter,
0.0005 inch; base diameter, 0.0015 inch; length, 0.020 inch; and the
half-angle of the conical section, 0.050. For the majority of the
models tested, the deviations were less than half of those given. The
machined and polished surfaces had average peak to trough roughnesses
of 20 microinches. In no case was there any correlation between the
scatter of the test results and the dimensional deviations of the models.


TESTS AND EQUIPMENT


These tests were conducted in the Ames supersonic free-flight wind
tunnel (reference 1) where models are fired from guns into still air or
upstream into a supersonic air stream. The models were launched from a
smooth-bore 20 mm gun, and were supported in the gun by plastic sabots
(fig. l(b)). Separation of the model from sabot was achieved by a
muzzle constriction which retarded the sabot and allowed the model to
proceed in free flight through the test section of the wind tunnel.
Drag coefficient was obtained by recording the time-distance history of
the flight of the model with the aid of a chronograph and four shadow-
graph stations at 5-foot intervals along the test section. From these
data, deceleration was computed and converted to drag coefficient.

With no air flow through the wind tunnel, Mach numbers varied from
1.2 to 4.2 depending on the model launching velocity. This condition is
referred to as "air off." Reynolds number varied linearly with Mach
number from 1.0 X 106 to 3.3 x 106, as shown in figure 2. With air flow
established in the wind tunnel, referred to as "air on," the combined
velocities of the model and Mach number 2 air stream, with the reduced
speed of sound in the test section, provided test Mach numbers
from 3.8 to 7.4. In this region of testing, Reynolds number was held
approximately at 4 X 106 by controlling test-section static pressure.
In addition, some models were tested at approximate Reynolds numbers
of 3 x 106 and 7.5 x 10 at Mach number 6.

The purpose of this investigation was to obtain drag data near
0 angle of attack. This report includes only the data from models
which had maximum observed angles of attack of less than 30 since larger
angles measurably increased the drag.

Since there are no known systematic errors, the accuracy of the
results is indicated by the repeatability of the data. Examination of
these data shows that repeat firings of similar models under almost
identical conditions of Reynolds number and Mach number yielded results
for which the average deviation from the faired curve was 1 percent and
the maximum deviation was 4 percent.







NACA EM A52B13


RESULTS AND DISCUSSION

Total Drag


Variation of the total drag coefficient with Mach number for each
of the models tested is presented in figure 3. No attempt was made to
join the air-off and air-on data due to differences in Reynolds number,
recovery temperature, and stream turbulence. Variation of drag coeffi-
cient with Mach number for all models is similar, in that the drag
coefficient continually decreased with increasing Mach number. There is,
however, a tendency for the blunter models to show less decrease in drag
coefficient with increasing Mach number.

These data have been cross-plotted in figure 4 to show the effect
of bluntness on total drag coefficient for various Mach numbers. The
nose bluntness for minimum drag shown by each curve decreases with
increasing Mach number. This is shown by the dashed curve. At Mach
number 1.2 the bluntness with minimum drag is 28 percent as compared to
11 percent at Mach number 7. At Mach numbers less than 1.5, drag penal-
ties for models with bluntnesses approaching 50 percent are moderate but
grow large with increasing Mach number. As Mach number becomes greater
than 4.5, the drag penalties for large bluntnesses do not increase meas-
urably but nevertheless are severe.

Drag in terms of volume may be important in some design consider-
ations. In order to indicate the relative merit of the models in terms
of drag for equal volume, the data of figure 4 have been replotted in
figure 5, where drag coefficient is referred to volume to the two-thirds
power. These curves show that moderate and even large bluntnesses (the
degree of bluntness depending on Mach number) may be used to decrease the
drag for equal volume.


Wave Drag


The variation of the total drag with model bluntness is believed to
result primarily from the variation of the wave drag of the models and to
be essentially independent of the base drag and skin-friction drag.
In order to show this, the wave drag of the blunt models was estimated
from the experiment by assuming the combined base drag and skin-friction
drag independent of bluntness and these results were compared to wave
drag determined by the method of Munk and Crown (reference 2). In the
estimation of the wave drag, the base drag and skin-friction drag used
were those of the cone, and were obtained by subtracting the theoretical
wave drag of the cone (reference 3) from the experimental total drag of
the cone at each Mach number. These values of combined base drag and







NACA RM A52B13


skin-friction drag were then subtracted from the total drag of the blunt
models to obtain the wave drag of each model. The results are shown by
the solid curves in figure 6, where wave drag is plotted as a function
of model bluntness.

In the method of Munk and Crown, the wave drag is computed by summing
up the momentum change through the head shock wave. Since part of the
wave shape is unaccounted for because of the limited field of view in
the shadowgraphs, an approximation suggested by Nucci (reference 4) was
used to estimate the wave drag omitted. This approximation gives the
upper and lower limits of the wave drag omitted. The mean value of these
limits was used in all cases. These results are indicated by the points
in figure 6. The mean disagreement between the results of this method
and the results obtained by assuming base drag and skin-friction drag
independent of bluntness is 7 percent.

Another method of estimating wave drag of the blunt models is by the
addition of the wave drag of a hemisphere to that of a conical afterbody.
Collected data showing the manner in which the wave drag of a hemisphere
varies with Mach number is shown in figure 7.1 The wave drag of the hemi-
spherical tip was obtained directly from this figure, and the wave drag
of the conical afterbody was obtained from the tables of reference 3.
The results of this method are presented as the dashed curves in figure 6.
A comparison of the results of this method with the results of the first
two methods shows that although the method of estimating wave drag by
the addition of the wave drag of a hemisphere to that of a conical after-
body appears to overestimate wave drag of the blunt models, it may
nevertheless be adequate for many engineering purposes.


Viscous Effects


The effect of Reynolds number on total drag coefficient was investi-
gated at Mach number 6. In figure 3, data for three Reynolds numbers,

'Wave drag of a hemisphere at Mach numbers from 1.05 to 1.40 was esti-
mated from the data of reference 5 by calculating the wave drag of the
pointed body and assuming that the drag due to the afterbody and fins
was not a function of nose shape. At Mach numbers of 15, 2.0, 3.0,
and 3.8, wave drag of a hemisphere was obtained from unpublished pres-
sure distributions from the Ames 1- by 3-foot supersonic wind tunnel.
Wave drag of a hemisphere at Mach numbers of 3.0, 4.5, 6.0, and 8.0 were
estimated from total drag measurements of spheres (reference 6) by sub-
tracting 70 percent of the maximum possible base drag and neglecting
skin-friction drag. The possible error introduced by estimating the
wave drag of the pointed body of reference 5 and the base drag of the
sphere is believed to be no greater than 4 percent.







NACA RM A52B13


3 X 106, 4 X 106, and 7.5 x 106 are included for cones and 50-percent
blunt models. For the cones, the drag coefficient increased approximately
10 percent with increasing Reynolds number. For the 50-percent blunt
models little or no change in drag coefficient was measured. The vari.
ation in drag coefficient for the cones was undoubtedly due to changes in
the boundary-layer flow on the models at varying Reynolds numbers, as
shown by the shadowgraphs in figure 8(a). At a Reynolds number of
3 x 106 the clearly defined wake (as indicated by the arrow in the
figure) is associated with laminar flow. At high Reynolds numbers, the
diffused wake indicates turbulent flow. Referring to figure 8(b), the
boundary-layer wakes of the 50-percent blunt models appear diffused and
turbulent at all Reynolds numbers. Since the wake of the 50-percent
blunt model at Reynolds number of 3 X 106 appears turbulent compared to
the laminar wake of the cone at this condition, it is concluded that
boundary-layer transition occurred at lower Reynolds numbers on the
50-percent blunt model than on the cone.

An interesting flaw phenomenon is illustrated in figure 9 by
shadowgraphs of two cones at Mach number 3.7. The shadowgraph in
figure 9(a) shows a smooth flow condition in contrast to a nonsteady
disturbed flow condition shown in figure 9(b). The disturbed flow seems
to consist of regions of turbulent air moving aft on the model surface,
with pressure waves attached to the leading edges of these regions.
Flow disturbance of this nature was observed occasionally on cones at
small angles of attack at Reynolds numbers of 2.5 X 106 and greater.
Cones with angles of attack in the order of 30 to 60 consistently had
disturbed flow. This flow condition occurred less often on blunt models
than on cones; and when present on blunt models, was always of slight
intensity. Data for models that exhibited this flow condition were not
included in this paper. The effect of flow disturbance on cones with
angles of attack of less than 30 was to raise the drag about 8 percent.
This increase in drag is attributed to increases in base drag as well as
wave drag.


CONCLUSIONS


From this investigation, the following conclusions were drawn for
spherically blunted conical models of fineness ratio 3:

1. Small amounts of spherical bluntness (nose diameters in the
order of 15 percent of base diameter) have been found to be beneficial
for reducing drag.

2. For large spherical bluntnesses (nose diameters in the order of
50 percent of base diameter) drag penalties were moderate at Mach numbers
of less than 1.5, but became severe with increasing Mach number.







NACA RM A52B13


3. Estimation of wave drag by combining experimental values of
wave drag of a hemisphere with wave drag of the conical surfaces is
believed to predict wave drag adequately for many engineering purposes.


Ames Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Moffett Field, Calif.


REFERENCES


1. Seiff, Alvin, James, Carlton S., Canning, Thomas N., and Boissevain,
Alfred G.: The Ames Supersonic Free-Flight Wind Tunnel.
NACA RM A52A24, 1952.

2. Munk, Max M., and Crown, J. Conrad: The Head Shock Wave. Naval
Ordnance Lab. Memo 9773, 1948.

3. Staff of the Computing Section, Center of Analysis, under the direc-
tion of Zdenek Kopal: Tables of Supersonic Flow Around Cones.
M.I.T. Tech. Rep. No. 1, Cambridge, 1947.

4. Nucci, Louis M.: The External-Shock-Drag of Supersonic Inlets Having
Subsonic Entrance Flow. NACA RM L50Gl4a, 1950.

5. Hart, Roger G.: Flight Investigation of the Drag of Round-Nosed
Bodies of Revolution at MachNumbers from 0.6 to 1.5 Using Rocket-
Propelled Test Vehicles. NACA RM L51E25, 1951.

6. Hodges, A. J.: The Drag Coefficient of Very High Velocity Spheres.
New Mexico School of Mines, Research and Devel. Div., Socorro,
New Mexico, Oct. 1949.




































Digitized by the Internet Archive
in 2011 with funding fion
University of Florida, George A. Smathers Libraries with support from LYRASIS and [he Sloan Foundation


http://www.archive.org/details/effectofbluntnes00ames






NACA RM A52B13


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NACA RM A52B13 13



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NACA RM A52B13


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NACA RM A52B13


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NACA RM A52B13


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Figure 8.- Shadowgraphs of cones and 50-percent blunt models at
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NACA RM A52B13


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Figure 9.- Shadowgraphs comparing smooth flow with disturbed flow
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